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While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which…

Machine Learning · Computer Science 2025-12-03 Yuandong Tian

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep…

Neural and Evolutionary Computing · Computer Science 2014-02-20 Andrew M. Saxe , James L. McClelland , Surya Ganguli

Regularization is crucial to the success of many practical deep learning models, in particular in a more often than not scenario where there are only a few to a moderate number of accessible training samples. In addition to weight decay,…

Machine Learning · Computer Science 2018-08-07 Che-Wei Huang , Shrikanth S. Narayanan

While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical…

The realization of complex classification tasks requires training of deep learning (DL) architectures consisting of tens or even hundreds of convolutional and fully connected hidden layers, which is far from the reality of the human brain.…

Machine Learning · Computer Science 2023-04-21 Yuval Meir , Ofek Tevet , Yarden Tzach , Shiri Hodassman , Ronit D. Gross , Ido Kanter

Policy-gradient methods are widely used in reinforcement learning, yet training often becomes unstable or slows down as learning progresses. We study this phenomenon through the noise-to-signal ratio (NSR) of a policy-gradient estimator,…

Optimization and Control · Mathematics 2026-02-10 Haoyu Han , Heng Yang

Deep neural networks are often trained in the over-parametrized regime (i.e. with far more parameters than training examples), and understanding why the training converges to solutions that generalize remains an open problem. Several…

Machine Learning · Statistics 2018-03-23 Hartmut Maennel , Olivier Bousquet , Sylvain Gelly

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

Machine Learning · Computer Science 2019-10-17 Mohammad Amin Nabian , Hadi Meidani

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest…

Machine Learning · Computer Science 2023-07-25 Ethan Caballero , Kshitij Gupta , Irina Rish , David Krueger

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

Current theoretical results on optimization trajectories of neural networks trained by gradient descent typically have the form of rigorous but potentially loose bounds on the loss values. In the present work we take a different approach…

Machine Learning · Computer Science 2021-05-04 Maksim Velikanov , Dmitry Yarotsky

We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks. We show that in the initial epochs, almost all of the performance…

Machine Learning · Computer Science 2019-05-29 Preetum Nakkiran , Gal Kaplun , Dimitris Kalimeris , Tristan Yang , Benjamin L. Edelman , Fred Zhang , Boaz Barak

Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome…

Adaptation and Self-Organizing Systems · Physics 2012-02-09 Neli Blagus , Lovro Šubelj , Marko Bajec

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…

We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation…

Statistical Mechanics · Physics 2009-10-31 JJ Ramasco , JM Lopez , MA Rodriguez

Scaling deep reinforcement learning networks is challenging and often results in degraded performance, yet the root causes of this failure mode remain poorly understood. Several recent works have proposed mechanisms to address this, but…

Deep learning experiments by Cohen et al. [2021] using deterministic Gradient Descent (GD) revealed an Edge of Stability (EoS) phase when learning rate (LR) and sharpness (i.e., the largest eigenvalue of Hessian) no longer behave as in…

Machine Learning · Computer Science 2022-10-31 Sanjeev Arora , Zhiyuan Li , Abhishek Panigrahi

Representation learning that leverages large-scale labelled datasets, is central to recent progress in machine learning. Access to task relevant labels at scale is often scarce or expensive, motivating the need to learn from unlabelled…

Machine Learning · Computer Science 2022-02-14 Arna Ghosh , Arnab Kumar Mondal , Kumar Krishna Agrawal , Blake Richards

Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent…

Machine Learning · Computer Science 2018-11-20 Farzan Farnia , Jesse M. Zhang , David Tse

In-context learning (ICL) enables large language models to adapt to new tasks from demonstrations without parameter updates. Despite extensive empirical studies, a principled understanding of ICL emergence at scale remains more elusive. We…

Machine Learning · Computer Science 2025-11-11 Sushant Mehta , Ishan Gupta